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How To Calculate The length And volume Of Semi Circular Arch

How To Calculate The length And volume Of Semi Circular Arch

Let us now calculate theĀ length & volumeĀ of the semi-circular arch as shown below.

 

Calculate The length And volume Of Semi Circular Arch

Given data:

The span of the semi-circular arch = 2m.

Height of arch = 1m.

Width of the arch = 300mm.= 0.3m.

Thickness of the arch = 230mm = 0.23m.

First, we will calculate the length of the arch

The arch length is calculated by the formula

=[Ā āˆ…Ā Ć— (2Ļ€rĀ Ć· 360Ā°)]

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Here

āˆ… = angle formed by the arch as shown below.

angle-of-arch

For a semi-circular arch, the value ofĀ āˆ…Ā =Ā 180Ā°

r = Radius of the arch.

Calculate the volume of the arch, let us calculate the radius of the center line as shown below.

arch-center-line

Radius

= [{arch span + (half of the arch width on both sides.)}Ć· 2 ]

= [{2m. + ( 2nos.Ɨ0.5 Ɨ 0.3m.)} Ć· 2]

= [{2m. + ( 0.3m.)} Ć· 2]

= [2.3m Ć· 2]

rĀ  =Ā 1.15m.

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1.Ā  Ā The arch length

=[Ā āˆ…Ā Ć— {(2Ļ€r) Ć· 360Ā°}]

=[180Ā° Ɨ {(2 Ɨ 3.142 Ɨ 1.15)Ć· 360Ā°}]

=[180Ā° Ɨ {7.227Ć· 360Ā°}]

(By cancelling 180Ā° & 360Ā° with each other)

= [ 7.227 Ć· 2 ]

=Ā 3.613m.

Now,

2.Ā The volume of the semi-circular arch

= [length Ɨ breadth Ɨ thickness]

= [3.613m. Ɨ 0.3m. Ɨ 0.23m.]

=0.249 CUM.

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About Raja Junaid Iqbal

Hi My name is Raja Junaid Iqbal and i am Land Surveyor by Profession but I've specialized in the field of Q,S and land development. As Professional Surveyor I engaged my self in all over the Gulf since 14 years.

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